30 pages, 15 figures, extended version of previous paper "Laplacian Change Point Detection for Dynamic Graphs" with novel material. arXiv admin note: substantial text overlap with arXiv:2007.01229
Dynamic graphs are rich data structures that are used to model complex relationships between entities over time. In particular, anomaly detection in temporal graphs is crucial for many real world applications such as intrusion identification in network systems, detection of ecosystem disturbances and detection of epidemic outbreaks. In this paper, we focus on change point detection in dynamic graphs and address three main challenges associated with this problem: i). how to compare graph snapshots across time, ii). how to capture temporal dependencies, and iii). how to combine different views of a temporal graph. To solve the above challenges, we first propose Laplacian Anomaly Detection (LAD) which uses the spectrum of graph Laplacian as the low dimensional embedding of the graph structure at each snapshot. LAD explicitly models short term and long term dependencies by applying two sliding windows. Next, we propose MultiLAD, a simple and effective generalization of LAD to multi-view graphs. MultiLAD provides the first change point detection method for multi-view dynamic graphs. It aggregates the singular values of the normalized graph Laplacian from different views through the scalar power mean operation. Through extensive synthetic experiments, we show that i). LAD and MultiLAD are accurate and outperforms state-of-the-art baselines and their multi-view extensions by a large margin, ii). MultiLAD's advantage over contenders significantly increases when additional views are available, and iii). MultiLAD is highly robust to noise from individual views. In five real world dynamic graphs, we demonstrate that LAD and MultiLAD identify significant events as top anomalies such as the implementation of government COVID-19 interventions which impacted the population mobility in multi-view traffic networks.
Iterative Views Agreement: An Iterative Low-Rank based Structured Optimization Method to Multi-View Spectral Clustering
The University of New South Wales（新南威尔士大学）；The University of Adelaide（阿德莱德大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；The University of Melbourne（墨尔本大学）；University of Technology Sydney（悉尼科技大学）
Speed-up and multi-view extensions to Subclass Discriminant Analysis
Faculty of Information Technology and Communication Sciences, Tampere University（坦佩雷大学信息技术与通信科学学院）；Programme for Environmental Information, Finnish Environment Institute（芬兰环境研究所环境信息项目）；Department of Engineering, Aarhus University（奥胡斯大学工程系）
Persistent Sheaf Laplacian Analysis of Protein Stability and Solubility Changes upon Mutation
Department of Mathematics, Michigan State University（数学系，密歇根州立大学）；The Frazer School（弗雷泽学校）；Lassiter High School（拉西特高中）；Department of Biochemistry and Molecular Biology, Michigan State University（生物化学与分子生物学系，密歇根州立大学）；Department of Electrical and Computer Engineering, Michigan State University（电气与计算机工程系，密歇根州立大学）
